TSTP Solution File: COL002-5 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : COL002-5 : TPTP v8.1.2. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:29:09 EDT 2024
% Result : Unsatisfiable 2.90s 1.76s
% Output : Refutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 20 ( 13 unt; 7 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 124 ( 2 ~; 0 |; 0 &; 122 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 22 ( 0 ^ 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(weak_fixed_point_type,type,
weak_fixed_point: $i > $i ).
thf(fixed_pt_type,type,
fixed_pt: $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(s_type,type,
s: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(i_type,type,
i: $i ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ s @ A ) @ B ) @ C )
= ( apply @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ s @ A ) @ B ) @ C )
= ( apply @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ c @ A ) @ B ) @ C )
= ( apply @ ( apply @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_definition) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ c @ A ) @ B ) @ C )
= ( apply @ ( apply @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
= ( apply @ A @ ( apply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
= ( apply @ A @ ( apply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( weak_fixed_point @ fixed_pt )
!= ( apply @ fixed_pt @ ( weak_fixed_point @ fixed_pt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
thf(7,plain,
( ( weak_fixed_point @ fixed_pt )
!= ( apply @ fixed_pt @ ( weak_fixed_point @ fixed_pt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [A: $i] :
( ( weak_fixed_point @ A )
= ( apply @ ( apply @ ( apply @ s @ ( apply @ c @ ( apply @ b @ A ) ) ) @ ( apply @ s @ ( apply @ c @ ( apply @ b @ A ) ) ) ) @ ( apply @ s @ ( apply @ c @ ( apply @ b @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',weak_fixed_point) ).
thf(18,plain,
! [A: $i] :
( ( weak_fixed_point @ A )
= ( apply @ ( apply @ ( apply @ s @ ( apply @ c @ ( apply @ b @ A ) ) ) @ ( apply @ s @ ( apply @ c @ ( apply @ b @ A ) ) ) ) @ ( apply @ s @ ( apply @ c @ ( apply @ b @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: $i] :
( ( apply @ i @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_definition) ).
thf(16,plain,
! [A: $i] :
( ( apply @ i @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
$false,
inference(cvc4,[status(thm)],[10,14,12,7,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : COL002-5 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n004.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 14:04:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.06/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/1.08 % [INFO] Parsing done (124ms).
% 1.40/1.09 % [INFO] Running in sequential loop mode.
% 1.72/1.33 % [INFO] eprover registered as external prover.
% 1.72/1.33 % [INFO] cvc4 registered as external prover.
% 1.88/1.34 % [INFO] Scanning for conjecture ...
% 1.95/1.39 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.95/1.41 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.95/1.42 % [INFO] Problem is propositional (TPTP CNF).
% 1.95/1.42 % [INFO] Type checking passed.
% 1.95/1.43 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 2.90/1.76 % External prover 'cvc4' found a proof!
% 2.90/1.76 % [INFO] Killing All external provers ...
% 2.90/1.76 % Time passed: 1219ms (effective reasoning time: 661ms)
% 2.90/1.76 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 2.90/1.76 % Axioms used in derivation (5): weak_fixed_point, c_definition, s_definition, b_definition, i_definition
% 2.90/1.76 % No. of inferences in proof: 13
% 2.90/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1219 ms resp. 661 ms w/o parsing
% 3.10/1.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.10/1.83 % [INFO] Killing All external provers ...
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